JOURNAL OF PHYSICS OF THE EARTH, Vol. 19, No. 1,

JOURNAL OF PHYSICS OF THE EARTH, Vol. 19, No. 1, 1971 1 Source Process of Deep and Intermediate Earthquakes as Inferred from Long-Period P and S Waveforms 1. Intermediate-depth Earthquakes in the Southwest Pacific Region Takeshi By MIKUMO Disaster Prevention Research Institute, Kyoto University Abstract The source process of four intermediate earthquakes with magnitudes of 6.0-6.8 and focal depths between 100 and 200km has been re-investigated from the analysis of long-period P and S waveforms. The source process times recovered from the times of the first half cycle of recorded P waves or the group delay times derived from the slopes of equalized phase spectrum show an azimuthal dependence with respect to the orientation of a nodal plane and of the null vector. If we assume shear dislocation models for these earthquakes, the dependence yields a solution to the problem of which of two nodal planes corresponds to the slip plane. Various source parameters have also been estimated from the azimuthal dependence by least squares technique. The dimension of the slip plane or the fault length and width range in 25-40km and 8-18 km, respectively, and the rise time of dislocation is found to be about 1sec. The rupture velocity might be as low as 3.2km/sec, if two-dimensional propagation is assumed. The theoretical seismograms of both direct P and S waves appropriate to each recording station have been synthesized on the basis of the estimated source parameters, taking into account the combined effects of wave propagation in the mantle and the crust and of the seismograph response. A good agreement of general features between the observed and synthesized waveforms on the three component seismograms gives support to the above slip dislocation model. Comparison of the amplitudes on the both kinds of seismograms of 80-140cm. The stress drop at these earthquakes ranges from 50 to 90 bars but might exceed 170 bars for one shock. The effective initial stress to produce shear dislocations is also estimated in relation to the frictional stress on the slip plane. Recent seismic observations covering a low frequency range and the introduction of elastic dislocation models have provided a powerful approach to clarify the dynamical process at the source not only of large shallow earthquakes, but also of deep-focus and intermediate-depth earthquakes that occurred between 100 and 600km (TENG and BEN-MENA- HEM, 1965; BOLLINGER, 1968; BERCKHEMER and JACOB, 1968; MIKUMO, 1969; FUKAO, 1970). It is expected that if the source of all these earthquakes can be interpreted in terms of shear dislocations, the stress-strain drop at the source, shear stresses causing these earth quakes, and their variations with depth will be estimated, and that the strength and thermal state of material in the mantle and their implications to the tectonic structure of a deep seismic zone, such as descending slabs of the lithosphere (ISACKS et al., 1968; MC- KENZIE, 1969), and the cause of deep and intermediate earthquakes might be brought into the light. It appears that there still remain unsolved problems on the observational side in an application of shear dislocation models to deep earthquakes. The problems are; whether the source is a moving dislocation, or at what velocity dislocations spread out over a slip plane formed in the mantle with increased temperature and pressure; and whether the radiation pattern of S waves including the absolute amplitudes and waveforms can be

2 explained by a dislocation source with the same parameters as for P waves. The purpose of the present paper is to elucidate more clearly the source process of intermediate-depth earthquakes, by making direct approach to the problems. The first step is to make an attempt to estimate the source parameters including the dimension, the amount of dislocation and the rupture velocity, from azimuthal variations of recorded P waveforms. The second approach is to synthesize theoretical seismograms of both P and S waves from dislocation sources with the estimated parameters, taking into account the combined effects of wave propagation in the earth and a recording instrument, and to compare them with their observed waveforms on the three-component records, in order to test the appropriateness of the assumed model. The stress drop at the time of these earthquakes and the initial stress to produce shear dislocations are discussed in some detail. The earthquakes analyzed here are four intermediate shocks that occurred along island arcs from New Guinea to the Fuji Islands at depths between 100 and 200km, which have been treated in a previous paper (MIKUMO, 1969). Relevant information is again listed in Table 1. Data used are the long-period vertical and two horizontal component seismograms recorded at the WWSSN stations. In the previous study (MIKUMO, 1969), theoretical seismograms of direct P waves have been synthesized from moving dislocation models with variously assumed source parameters through a linear filter system composed of the earth and instrument, and compared with the corresponding records. The comparison has shown that the average waveform on the records is similar to that from a double-couple point source with a ramp yielded the seismic moment and probable ranges for some other parameters. Closer examinations reveal, however, some difference in the recorded P waveforms for the first half-period as well as in the slope of the equalized phase spectrum (MIKUMO 1969), depending on the location of recording stations with respect to the source. For this reason, an attempt is made here to evaluate the possible azimuthal dependence of the above two quantities. Although the waveforms are predominantly controlled by the seismograph characteristics, we assume that there are no serious differences in its frequency response among the stations. This assumption may be justified by the fact that the shape of calibration pulses placed on seismograms is almost identical at these stations. (1) The slope of the phase spectrum (or the group delay time) The equalized source phase spectrum of direct P waves has been given in Fig. 19 in the previous paper, for all stations in the four earthquakes mentioned. It can be seen that there are appreciable differences in the slope of the spectrum, and a possibility has been suggested that the source dimension could in principle be evaluated from the slopes if the initial phase correction is made for a spherical earth. The correction gives a constant term independent on frequency on the standpoint of normal modes (BRUNE, 1964; SATO, 1969), and hence yields no effects on the Table 1. Information of the earthquakes analyzed.

Fig. 1. Group delay times, observed first half-periods, and source process times. (a) No. 15 (b) No. 23

4 Takeshi MIKUMO rected for a standard structure of HASKELL (1960).). A difference of 10km in the crustal thickness yields the change of about 1.5sec in the group delay time. ii) The corrected phase spectra do not change monotonously with frequency; and iii) The initial time of digitization might not exactly agree with the arrival time of first P waves when they have a blunt beginning. It would therefore be rather difficult to rely on the group delay times in a precision determination of the source parameters. (b) Source process time Another method is to infer from observed records the apparent time duration of energy release at the source region or the total time of faulting process, which is specified by the source finiteness and the rise time of dislocation. The displacement of P waves ur0(t) at great distances from dislocation sources may be expressed by (MIKUMO, 1969), (3) (4) Fig. 2. Relation between first half-periods and the source process times. where (5) (6) (7)

Source Process of Deep and Intermediate Earthquakes 5 Table 2. Source process times and direction cosines

not used here. The open circles plotted in the lower part of Figs. 1(a) and 1(b) are the source process times T0 thus estimated from t on the indivisual records. It can be seen that the plotted points show a good consistency with point and the front of it travels two-dimensionally at a constant velocity ƒò as the above stated reasons, we use the source illustrated process times obtained from this time domain analysis, rather than the group delay times from the frequency domain analysis to evaluate the source parameters. Estimation of Source Parameters The source process times thus estimated at a number of stations for the four earthquakes are tabulated in Table 2, together with the direction cosines of the station azimuth with respect to the normals to two nodal planes and to the null vector respectively. The uncertainty of the process times due to measurement errors and to allowance in the relation between t and T0 is of the order of 0.5-1.0sec. It is found that T0 ranges from almost zero to about 4sec and sometimes reaches 6 sec, although the average has been estimated as 2-3 sec (MIKUMO, 1969). Since differences in local crustal structures and in attenuations make only a difference of To less than the above uncertainty, we take the interpretation that the rather large variations of T0 result from azimuthally asymmetric source dimension and rupture propagation. We shall now examine the possible azimuthal dependence of T0. The dependence has been tested with respect to the three directions given in the above table, to determine which of the two nodal planes corresponds to the slip plane. It has been found for each of the four earthquakes, as shown in Figs. 3(a) `3(d), that there are some linear relations with considerable scatter between tern of P wave first motions. The next step is to evaluate four unknown do not know the direction of rupture propagation at this stage. For this reason, we assume here that the rupture starts from a in Fig. 4(a). This assumption may be understood as bidirectional faulting (OTSUKA, 1964; HIRASAWA and STAUDER, 1965; FUKAO, private communication, 1970) in which the rupture propagates with different velocities along the longer and and shorter sides of the slip plane. In this case, eq. (8) may be rewritten in a more general form, Fig. 4(a). Geometry for an assumed rupture process.

8 amount of dislocation D can also be estimated from the seismic moment or DLW, which has been determined in the previous paper (1969; See also Corrections, 1970) from comparison and Lk can be estimated with rather large uncertainty by assigning an appropriate value to the compressional velocity around the source region. The estimated length L (the longer one of the two length Lj and Lk) of the slip plane ranges from 25 to 42 km, while its width W (the shorter one of Lj and Lk) is about 6 to 20km, being the order of 1/2 `1/4 of the length, except for earthquake No. 12. The results show that the slip plane has a longer dimension in the slip direction for earthquake No. 15, but it does in the direction of the null vector for earthquakes Nos. 6 and 23. In the case of earthquake No. 12, the dimension has a comparable order in the two directions. Once the dimensions were determined, the between the double amplitudes of the recorded and synthesized P waves. The estimated amount is 70 `100cm for three earthquakes and reaches 140cm for earthquake No. 15. On the other hand, we cannot uniquely respectively, where two curves from one earthquake give the upper and lower bounds Fig. 4(b). Relation between the apparent rupture velocity and the rise time of dislocation.

Source Process of Deep and Intermediate Earthquakes 9 that come from probable errors in the adopted dimension. If all the four earthquakes occur through the dynamical process with similar The stress drop during these earthquakes has also been estimated by using the obtained source parameters. For a dip-slip displace- placement over the entire fault surface. Earth- quake No.15 would correspond to the former case, and the latter may be applied to earth- quakes Nos. 6, 12 and 23. The above equations assume, however, an infinitely long fault. It may be more appropriate to consider a cir- Fig. 5. Fault-plane solutions.

where these components are taken positive in the directions away from the origin, away Fig, 6. Nodal curves of P, SV and SH waves, (a) No. 12 (b) No. 15

12 Takeshi MIKUMO

Source Process of Deep and Intermediate Earthquakes 13 Fig. 8. Observed and synthesized seismograms (three components of P and S waves) (a) earthquake No. 12.

14 Takeshi MIKUMO Fig. 8. Observed and synthesized seismograms (three components of P and S waves) (b) earthquake No. 15.

Source Process of Deep and Intermediate Earthquakes 15 short-period oscillations are removed by a proper filtering, the agreement would be much improved. It is more appropriate to make such a comparison on the three component seismograms, since a different kind of information is involved in the horizontal records, particularly of S waves. It is, however, usually difficult to see well-isolated direct S waves on all of the three components at many stations. This is because they are often contaminated by preceding motion of P wave group and later phases such as ss and ScS over a wide range of epicentral distances, and partly because SV waves are sometimes distorted by the crust due to large incident angles. For this reason, the comparison can be made only for a limited number of stations, whereas FUKAO (1970) estimated the fault parameters directly from S waveforms at many stations. Two horizontal components fn(t) and fe(t) on the synthesized seismograms are derived by the rotation of axis, (17)

16 Takeshi MIKUMO

Source Process of Deep and Intermediate Earthquakes 17 Acknowledgments I have benefited from stimulate discussions with Drs. Yoshio Fukao and Katsuyuki Abe of the Earthquake Research Institute, and Mr. Kazuo Oike at our Institute. I wish to thank Dr. Michio Otsuka of Kumamoto University for valuable suggestions at an early stage of this study. My thanks are also extended to Mrs. Ritsuko Koizumi for assistance in the present work. Computations were made on a FACOM 230-60 at the Data Processing Center, Kyoto University. References Aki, K., Generation and propagation of G wave from the Niigata earthquake of June 16, 1964, Part 2. Estimation of earthquake moment, released energy and stress-strain drop from the G wave spectrum, Bull. Earthq. Res. Inst., 44, 73-88, 1966. Anderson, D.L., A. Ben-Menahem and C.B. Archambeau, Attenuation of seismic energy in the mantle, J. Geophys. Res., 70, 1441-1448, 1965. Benioff, H., Source wave form of three earthquakes, Bull. Seism. Soc. Amer., 53, 893-904, 1963.

18 Takeshi MIKUMO Berckhemer, H. and K.H. Jacob, Investigation of the dynamical process in earthquake foci by analyzing the pulse shape of body waves, Proc. of the X Assembly of the ESC, Sept., 1968, II, 253-352, 1970. Bollinger, G.A., Determination of earthquake fault parameters from long-period P waves, J. Geophys. Res., 73, 785-807, 1968. Bollinger, G.A., Fault length and fracture velocity for the Kyushu, Japan, earthquake of October 3, 1963, J. Geophys. Res., 75, 955-964, 1970. Brune, J., Travel times, body waves and normal modes of the earth, Bull. Seism. Soc. Amer., 54, 2099-2127, 1964. Brune, J., Seismic moment, seismicity, and rate of slip along major fault zones, J. Geophys. Res., 73, 777-784, 1968. Brune, J., Tectonic stress and the spectra of seismic shear waves from earthquakes, J. Geophys. Res., 75, 4997-5009, 1970. Brune, J. and C.R. Allen, A low stress-drop, lowmagnitude earthquake with surface faulting: The Imperial, California, earthquake of March 4, 1966, Bull. Seism. Soc. Amer., 57, 501-514, 1967. Brune, J.N., T.L. Henrey and R.F. Roy, Heat flow, stress and rate of slip along the San Andreas Fault, California, J. Geophys. Res., 74, 3821-3827, 1969. Burridge, R. and L. Knopoff, Body force equivalents for seismic dislocations, Bull. Seism. Soc. Amer., 54, 1875-1888, 1964. Burridge, R., Theoretical seismic sources and propagating brittle cracks, J. Phys. Earth, 16, Special Issue, 83-92, 1968. Dennis, J.G. and C.T. Walker, Earthquakes resulting from metastable phase transitions, Tectonophysics, 2, 401-405, 1965. Eshelby, J.D., Supersonic dislocations and dislocations in dipersive media, Proc. Phys. Soc. London, B 69, 1013-1019, 1956. Eshelby, J.D., The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roy Soc. London, A 241, 376-396, 1957. Evison, F.F., On the occurrence of volume change at the earthquake source, Bull. Seism. Soc. Amer., 57, 9-26, 1967. Fukao, Y., Focal process of a deep focus earthquake as deduced from long-period P and S waves, Bull. Earthq. Res. Inst., 48, 707-727, 1970. Griggs, D.T. and D.W. Baker, The origin of deepfocus earthquakes, in Properties of Matter, pp. 23-42, John Wiley & Sons, New York, 1969. Haskell, N.A., Crustal reflection of plane SH waves, J. Geophys. Res., 65, 4147-4150, 1960. Haskell, N.A., Crustal reflection of P and SV waves, J. Geophys. Res., 67, 4751-4767, 1962. Haskell, N.A., Total energy and spectral density of elastic wave radiation from propagating fault, Bull. Seism. Soc. Amer., 54, 1811-1841, 1964. Hirasawa, T. and W. Stauder, On the seismic body waves from a finite moving source, Bull. Seism. Soc. Amer., 55, 237-262, 1965. Isacks, B,J. Oliver and L.R. Sykes, Seismology and the new global tectonics, J. Geophys. Res., 73, 5855-5899, 1968. Keylis-Borok, V.I., The determination of earthquake mechanism, using both longitudinal and transverse waves, Ann. Geofis., 10, 105-128, 1957. Keylis-Borok, V.I., On estimation of the displacement in an earthquake source and of source dimensions, Ann. Geofis., 12, 205-214, 1959. Knopoff, L., Energy release in earthquakes, Geophys. J., 1, 44-52, 1958. Maruyama, T., On the force quivalents of dynamical elastic dislocations with reference to the earthquake mechanism, Bull. Earthq. Res. Inst., 41, 467-486, 1963. Mansinha, L., The velocity of shear fracture, Bull. Seism. Soc. Amer., 54, 369-376, 1964. McKenzie, D.P, Speculations on the consequences and causes of plate motions, Geophys. J., 18, 1-32, 1969. Mikumo, T., Mechanism of local earthquakes in Kwanto region, Japan, derived from the amplitude relation of P and S waves, Bull. Earthq. Res. Inst., 40, 399-424, 1962. Mikumo, T. and T. Kurita, Q distribution for longperiod P waves in the mantle, J. Phys. Earth, 16, 11-29, 1968. Mikumo, T., Long-period P waveforms and the source mechanism of intermediate earthquakes, J. Phys. Earth, 17, 169-192, 1969; Correction, ibid., 18, 313, 1970. Orowan, E., Mechanism of seismic faulting in rock deformation, A Symposium, Geol. Soc. Amer. Mem., 79, 323-345, 1960. Otsuka, M., Study on focal mechanism by the analysis of seismic waves of S-type, Spec. Contr. Geophys. Inst., Kyoto Univ., 4, 37-49, 1964. Randall, M.J., Seismic radiation from a sudden phase transition, J. Geophys. Res., 71, 5297-5302, 1966. Sato, Y.,T. Usami and M. Landisman, Theoretical seismograms of spheroidal type on the surface of a gravitating elastic sphere, II. Case of Gutenberg-Bullen A' earth model, Bull. Earthq, Res. Inst., 45, 601-624, 1967.

Source Process of Deep and Intermediate Earthquakes 19 Sato, R., Amplitude of body waves in a heterogeneous sphere, comparison of wave theory and ray theory, Geophys. J., 17, 527-544, 1969. Savage, J. C., The effect of rupture velocity upon seismic first motions, Bull. Seism. Soc. Amer., 55, 263-275, 1965. Savage, J. C., Radiation from a realistic model of faulting, Bull. Seism. Soc. Amer., 56, 577-592, 1966. Teng, T. L. and A. Ben-Menahem, Mechanism of deep earthquakes from spectrums of isolated bodywave signals, 1. Banda Sea earthquake of March 21, 1964, J. Geophys. Res., 70, 5157-5170, 1965. T., Y. Sat6 and M. Landisman and T. Odaka, Theoretical seismograms of spheroidal type on the surface of a gravitating elastic sphere, III. Case of a homogeneous mantle with a liquid core, Bull. Earthq. Res. Inst., 46, 791-819, 1968. Weertman, J., Dislocation motion on an interface with friction that is dependent on sliding velocity, J. Geophys. Res., 74, 6617-6622, 1969. Wyss, M., and J. N. Brune, Seismic moment, stress, and source dimensions from earthquakes in the California-Nevada region, J. Geophys, Res., 73, 4681-4694, 1968. Wyss, M., Stress estimates for South American shallow and deep earthquakes, J. Geophys. Res., 75, 1529-1544, 1970. (Received September 29., 1970; revised December 26, 1970)